Senator Ben Sasse also confirmed Trump's surprise move.
"We should be leading TPP," Sasse said. "China is a bunch of cheaters and the best way to push back on their cheating would be to be leading all these other rule-of-law nations in the Pacific that would rather be aligned with the U.S. than with China."
Engaging in talks to reenter the TPP would be part of a broader White House strategy to respond to an escalating trade flap between Trump and Beijing. Trump is looking for ways to crack down on what he believes are unfair trade practices in China, but he is having a hard time rallying other countries to backstop his push to impose new tariffs or raise the costs of exports and imports for China.
The president is also running into strong pushback from Republican lawmakers, particularly those representing agricultural regions where China's threatened retaliation against US exports would hit hard.
The TPP is a trade agreement the United States, Canada, Mexico, Japan, Vietnam, Singapore, Australia, and a number of other countries signed in early 2016, aiming to strengthen was meant to strengthen economic ties between the countries and give them more leverage in dealing with China.
The agreement never went into effect, however, because Trump withdrew from it three days after he was sworn in. The remaining countries still ratified a version of the TPP without the United States earlier this year.
Trump has never fully articulated what he opposed about the TPP, but he has shown a general reluctance to enter into multilateral trade deals because he believes these allow the United States to be ripped off.
"The Trans-Pacific Partnership is another disaster done and pushed by special interests who want to rape our country," Trump said in June 2016. "Just a continuing rape of our country. That's what it is, too. It's a harsh word - it's a rape of our country. This is done by wealthy people that want to take advantage of us and that want to sign another partnership."
Trump was not the only one to oppose TPP during the campaign. His Democratic rival, Hillary Clinton, also said she did not plan on ratifying the deal, even after she had a role in its formation during her time as President Barack Obama's Secretary of State.
Before Trump's election, efforts to ratify the deal had stalled in Congress.
In May 2016, as domestic political support for TPP was starting to erode, Obama wrote an op-ed in The Washington Post aiming to rally support.
"Increasing trade in this area of the world would be a boon to American businesses and American workers, and it would give us a leg up on our economic competitors, including one we hear a lot about on the campaign trail these days: China," he wrote.
Trump did not give Japan, one of the U.S.'s closest allies, an exemption from new steel and aluminium tariffs, making it less likely that they would rush to the White House's defence during a trade war.
But entering into a new TPP could unify Trump with other trading partners and put new pressure on Beijing to either allow more imports into China or risk being alienated by other Asian countries, that would now receive new trade benefits as part of the deal.
Still, it remains to be seen what exactly Trump would want to see in a new TPP, or whether the idea is just a passing fancy for the White House or a serious initiative they plan to launch.
"If it holds until this afternoon, that's a good move," remarked Senator Jeff Flake, a free trade advocate who was not at the White House meeting.
In February, Treasury Secretary Steven Mnuchin said the US was interested in reentering the trade agreement, but he quickly backed off those comments, making it sound like a deal would not materialise.
